Fact-checked by Grok 2 weeks ago

Coefficient of performance

The is a that measures the of devices such as , , and air conditioners by expressing the ratio of the desired transfer ( removed or added) to the work input required to achieve it. For a , which transfers from a low-temperature to a high-temperature one, the is defined as COP_R = |Q_C| / W, where Q_C is the magnitude of extracted from the cold and W is the work done on the system. In contrast, for a , which delivers to a high-temperature , the is COP_HP = |Q_H| / W, where Q_H is the magnitude of supplied to the hot , noting that Q_H = |Q_C| + W by of , which implies COP_HP = COP_R + 1. Unlike thermal efficiencies of heat engines, which are always less than 1, COP values can exceed 1 because they compare output to input work rather than to a heat source. The theoretical maximum COP for reversible (Carnot) cycles sets the performance benchmark, derived from the second law of thermodynamics. For a Carnot refrigerator operating between temperatures T_C (cold reservoir in ) and T_H (hot reservoir), COP_R,Carnot = T_C / (T_H - T_C). Similarly, for a Carnot , COP_HP,Carnot = T_H / (T_H - T_C). Real devices achieve lower COPs due to irreversibilities like and losses, but these limits guide design in applications such as building heating, cooling systems, and industrial processes. COP is a key metric in evaluating standards, with higher values indicating better performance relative to .

Introduction and Fundamentals

Definition

The coefficient of performance (COP) is a measure of the efficiency of heat transfer devices, such as refrigerators and heat pumps, defined as the ratio of the desired energy output—typically the heat delivered for heating or removed for cooling—to the work input required to achieve that transfer. Unlike thermal efficiency, which quantifies the fraction of heat input converted to useful work in heat engines and is always less than 1, COP applies to systems that use work to move heat rather than generate it from combustion or other sources. A key feature of COP is that its value can exceed 1, often significantly, because these devices amplify the effect by transferring from a low-temperature (such as the ) using a relatively small amount of work, rather than converting directly into work as in engines. This amplification arises from the thermodynamic principle that work input enables the relocation of a larger quantity of , making COP a metric of how effectively the device leverages external sources or sinks. In practice, COP is applied to various systems: for refrigerators, it represents the cooling provided relative to work input; for heat pumps, it measures the heating delivered; and for air conditioners, it similarly assesses cooling efficiency in controlled environments. These applications rely on fundamental thermodynamic concepts, where is the transfer of energy driven by temperature differences between systems, and work is the ordered energy transfer through mechanical or electrical means, such as in a refrigeration cycle.

Historical Context

The foundations of the coefficient of performance (COP) concept emerged in the context of 19th-century thermodynamics, building on Sadi Carnot's seminal 1824 work, Reflections on the Motive Power of Fire, which analyzed the efficiency of heat engines through the ideal Carnot cycle and implicitly extended to reversed cycles for refrigeration by demonstrating the limits of thermal energy conversion. Although Carnot focused on engine efficiency rather than explicitly defining COP for cooling or heating, his cycle provided the theoretical basis for later performance ratios in non-engine thermal devices. In 1852, William Thomson (Lord Kelvin) advanced this by proposing a reversed Carnot cycle as a practical "warming machine" for heating applications, effectively introducing early notions of performance metrics for heat transfer systems that exceeded unity efficiency. By the early , as and technologies proliferated for commercial and residential use, COP evolved from theoretical ratios to a practical tool in HVAC , with organizations like the American Society of Refrigerating Engineers (founded ) incorporating similar efficiency measures in standards for system evaluation. In 1958, the Air-Conditioning and (ARI) initiated the first performance rating standard for heat pumps, incorporating COP as a key metric. The standardization of COP accelerated after the 1959 formation of the American Society of Heating, Refrigerating and Air-Conditioning Engineers () through the merger of predecessor groups, which began formalizing as a key metric in post-1950s handbooks and guidelines for HVAC equipment testing and rating. This evolution culminated in broader regulatory adoption during the 1970s energy crises, particularly the 1973 oil embargo, which prompted to publish Standard 90-75 in 1975—the first national code for buildings—emphasizing in HVAC systems to reduce amid soaring fuel costs and national policy shifts toward conservation.

Mathematical Formulation

Basic Equation

The coefficient of performance (COP) is expressed by the general equation \text{COP} = \frac{|Q_\text{desired}|}{|W_\text{input}|}, where Q_\text{desired} represents the magnitude of the desired heat transfer (the cooling load for a refrigerator or the heating load for a heat pump), and W_\text{input} is the magnitude of the work supplied to the device, typically via a compressor or pump. This formulation derives from the first law of thermodynamics applied to a steady-state cyclic process, where the change in over the complete cycle is zero: \Delta U = 0 = Q_\text{net} - W_\text{net}. For such systems, the net Q_\text{net} equals the desired absorbed minus the rejected to the surroundings (Q_\text{desired} - Q_\text{rejected}), and the net work W_\text{net} corresponds to the input work (with W_\text{input} = Q_\text{rejected} - Q_\text{desired} after rearranging). Thus, the COP emerges as the ratio of the desired to the required work input. This contrasts with the \eta = W_\text{output}/Q_\text{supplied} for heat engines, where work is produced from , rather than consumed to transfer against a . In thermodynamic sign conventions, heat Q is taken as positive when added to the system (absorbed) and negative when removed (rejected), while work W is positive when performed by the system and negative when performed on the system; the first law is thus \Delta U = Q - W. For COP, however, magnitudes are employed to emphasize the practical ratio of useful thermal effect to energy expenditure, avoiding sign ambiguities in cycle analysis. For illustration, a device that provides 3 kW of cooling effect with 1 kW of work input yields a of 3, indicating three units of cooling per .

Variations for Different Systems

The coefficient of performance () is adapted differently depending on the specific , reflecting whether the primary goal is cooling or heating. For refrigerators and air conditioners, which aim to extract from a to maintain a lower , the is defined as the ratio of the heat absorbed from the cold space (Q_c) to the net work input (W), expressed as \mathrm{COP}_R = \frac{Q_c}{W}. This formulation emphasizes the cooling benefit relative to the energy expended, where typical values range from 2 to 4 for practical systems operating between standard indoor and outdoor temperatures. In contrast, for heat pumps, which deliver heat to a warmer space for heating purposes, the COP is defined as the ratio of the heat delivered to the hot reservoir (Q_h) to the net work input (W), given by \mathrm{COP}_H = \frac{Q_h}{W}. From the first law of and energy balance in a closed , where Q_h = Q_c + W, it follows that \mathrm{COP}_H = \mathrm{COP}_R + 1, highlighting how the same device can serve dual roles with interrelated performance metrics. For reversible cycles in combined systems, such as those approximating ideal heat engines operated backward, the COP takes a general temperature-dependent form for the ideal case: \mathrm{COP} = \frac{T_\text{desired}}{T_\text{hot} - T_\text{cold}}, where temperatures are in , T_\text{desired} is the target (T_\text{cold} for cooling or T_\text{hot} for heating), T_\text{hot} is the higher , and T_\text{cold} is the lower one. This expression provides the theoretical benchmark for systems like vapor-compression cycles in both and heat pumping applications. Notation variations exist in standards, particularly with the Energy Efficiency Ratio (EER), a non-SI metric used in some regulatory contexts for , defined as in British thermal units per hour (BTU/h) divided by power input in watts. EER relates to through the conversion factor \mathrm{COP} = \frac{\mathrm{EER}}{3.412}, accounting for unit differences, allowing comparison across standards while the underlying physics remains consistent with the SI-based .

Theoretical Maximums

Carnot Efficiency Limits

The represents the theoretical benchmark for the maximum efficiency of heat engines and refrigerators, establishing the upper limits on the coefficient of performance () for thermodynamic systems operating between two temperature reservoirs. Derived from the principles of reversible processes, the consists of two isothermal and two adiabatic steps, ensuring no net in the system and surroundings. This reversibility, governed by the second law of thermodynamics, implies that any real system deviating from this ideal will have a lower . For a refrigerator, which extracts heat Q_c from a cold reservoir at temperature T_c and rejects heat Q_h to a hot reservoir at T_h (with T_h > T_c), the Carnot COP is the maximum achievable value. The derivation begins with the entropy balance for a reversible cycle: the total change in entropy \Delta S = 0. Heat absorption at the cold reservoir contributes +Q_c / T_c to entropy, while rejection at the hot reservoir contributes -Q_h / T_h. Setting \Delta S = 0 yields Q_c / T_c = Q_h / T_h, or Q_h / Q_c = T_h / T_c. The work input is W = Q_h - Q_c, so the COP for refrigeration is \text{COP}_{R,\text{Carnot}} = Q_c / W = Q_c / (Q_h - Q_c) = 1 / (T_h / T_c - 1) = T_c / (T_h - T_c), where temperatures are in absolute scale (Kelvin). This formula shows that the COP increases as the temperature difference T_h - T_c decreases, approaching infinity for infinitesimal differences, as the second law permits arbitrarily efficient heat transfer near thermal equilibrium. For a , which delivers heat Q_h to the hot reservoir by absorbing Q_c from the cold one, the Carnot COP follows similarly from the same balance. Substituting into the \text{COP}_{H,\text{Carnot}} = Q_h / W, the result is \text{COP}_{H,\text{Carnot}} = (Q_h / Q_c) / (Q_h / Q_c - 1) = (T_h / T_c) / (T_h / T_c - 1) = T_h / (T_h - T_c). Again, the COP diverges as T_h approaches T_c, highlighting the fundamental imposed by gradients. To illustrate, consider a refrigerator operating between T_c = 273 K (0°C) and T_h = 293 K (20°C). The Carnot COP is $273 / (293 - 273) = 273 / 20 = 13.65, which exceeds typical real-world values by a significant margin due to irreversibilities in practical systems.

Deviations from Ideal Performance

In real-world refrigeration and heat pump systems, the coefficient of performance (COP) falls short of the ideal Carnot limits due to inherent irreversibilities that generate entropy and degrade available work potential. These include mechanical friction in components like compressors and pumps, unintended heat leaks across insulation or piping, and finite-rate heat transfer processes that require non-zero temperature gradients to achieve practical rates. Such irreversibilities typically reduce the COP to 30-60% of the Carnot value, corresponding to a performance shortfall of 40-70% relative to the theoretical maximum. External irreversibilities, arising from heat transfer across finite temperature differences between the system and reservoirs, and internal ones, such as frictional losses within the cycle, collectively account for this degradation. The second law efficiency provides a standardized to assess these deviations, defined as the ratio of the actual to the Carnot : \eta_{II} = \frac{\mathrm{COP_{actual}}}{\mathrm{COP_{Carnot}}} For commercial refrigeration and systems, \eta_{II} ranges from 30% to 60%, reflecting the balance between thermodynamic ideals and practical constraints like component sizing and operating speeds. This highlights how closely a system approaches reversibility; values below 30% indicate significant opportunities for improvement through design refinements, while those above 60% are rare outside laboratory conditions. In screw chillers, for instance, reveals second law efficiencies clustering in the 40-50% range, with major losses in the and heat exchangers. Temperature approach differences in heat exchangers represent a primary source of irreversibility, as finite exchanger sizes demand a minimum \Delta T to drive at viable rates. In the evaporator, the is typically 5-10 below the cooled space to maintain , creating an effective temperature lift greater than the minimum required and thus lowering . Similarly, in the , a 5-10 approach above the exacerbates work. These differences, while necessary for compact designs, can reduce by 10-20% compared to idealized infinite-area exchangers. In vapor-compression cycles, cycle-specific losses further compound deviations from ideal performance. Pressure drops across and coils, due to flow resistance, elevate the and reduce mass flow rates, increasing power input without equivalent gains in and thereby decreasing COP by up to 5-10% in typical systems. in the prevents liquid but, if beyond 5-10 , diminishes the specific refrigerating effect by replacing useful with sensible heating of vapor. Conversely, in the enhances liquid density and capacity but introduces losses if the degree exceeds 5-10 , as it may stem from over-sized condensers or suboptimal controls. These effects underscore the trade-offs in optimizing cycle components for real operating conditions.

Practical Considerations

Factors Affecting COP

The coefficient of performance (COP) in heat pumps and refrigeration systems is highly sensitive to temperature differences between the heat source and sink, with efficiency declining as the temperature lift—defined as the absolute difference |T_h - T_c|—increases. For instance, air-source heat pumps exhibit reduced in extreme cold climates, where lower outdoor temperatures increase the required work input for the to maintain indoor heating, often dropping COP values to 2.0-3.0 at temperatures around -10°C, depending on system design and load. This dependency arises because colder evaporator temperatures reduce refrigerant evaporation rates and increase compression ratios, leading to higher relative to heat output. Refrigerant properties play a critical role in determining cycle efficiency through their thermodynamic characteristics, such as latent heat of vaporization, critical temperature, and vapor density. s with higher enable greater heat absorption per unit mass in the , potentially improving by enhancing the refrigerating effect, while those with suitable critical temperatures allow operation across wider temperature ranges without exceeding pressure limits. For example, hydrofluoroolefins (HFOs) can yield comparable to traditional hydrofluorocarbons (HFCs) with better volumetric in some systems, though vapor density influences pressure drops in system , indirectly affecting overall . System design elements, particularly compressor and heat exchanger configurations, significantly influence real-world COP by minimizing irreversibilities in the vapor-compression cycle. Compressor efficiency, often measured as the isentropic efficiency (the ratio of ideal isentropic work to actual work), directly impacts COP; higher efficiencies (e.g., above 80%) reduce energy losses from non-ideal compression processes, which deviate from adiabatic ideals and generate excess heat. Similarly, proper sizing of heat exchangers ensures adequate heat transfer surfaces: undersized evaporators or condensers lead to higher approach temperatures and reduced COP, whereas optimal sizing can increase COP by up to 15% through improved refrigerant flow and reduced pressure losses. Oversized systems, however, may exacerbate inefficiencies under varying conditions. Load variations, especially in part-load conditions, can degrade COP in non-inverter systems due to frequent on/off cycling. When heating or cooling demand falls below full capacity, fixed-speed cycle intermittently, incurring startup losses from motor inrush currents and migration, which lower average efficiency compared to steady-state operation. Studies show that such cycling in oversized units can reduce seasonal COP by 10-20% relative to modulated systems, as partial-load performance suffers from incomplete during short cycles and increased auxiliary energy use for fans and controls. Inverter-driven systems mitigate this by varying compressor speed, but non-inverter designs remain common in cost-sensitive applications, highlighting the need for load-matching in system selection.

Methods to Enhance COP

One key strategy to enhance the coefficient of performance (COP) in and systems involves the use of variable-speed compressors, often implemented through inverter technology. These compressors adjust their rotational speed to match the varying thermal loads, avoiding the inefficiencies of on-off cycling in fixed-speed units and maintaining operation closer to optimal conditions. This approach can boost COP by 20-30% in heating mode, particularly during part-load scenarios common in residential and commercial applications. Selecting advanced refrigerants with low (GWP) also plays a crucial role in improving COP by better aligning thermodynamic properties with system requirements. Natural refrigerants such as (CO₂) excel in transcritical cycles for medium- to high-temperature applications, offering higher efficiency due to superior and in subcritical conditions. Hydrocarbons like (R-290) provide comparable or slightly higher COPs to traditional hydrofluorocarbons (HFCs) in low-temperature refrigeration, with energy savings of up to 10-15% in some configurations owing to their favorable and lower compression ratios. Regulatory frameworks, such as the to the and the US AIM Act (as of 2025), mandate HFC phase-downs, promoting low-GWP refrigerants that support COP enhancements through optimized system compatibility. Incorporating heat recovery mechanisms and multi-stage cycle configurations further elevates overall system , especially when addressing large temperature differences () between heat sources and sinks. Cascade systems, which stack multiple stages with intermediate heat exchangers, enable efficient operation across wide ranges—such as in —by optimizing each stage's pressure and temperature, potentially increasing by 18-37% over single-stage alternatives. recovery in these setups captures from the condenser or compressor discharge for preheating or other uses, reducing the net energy input and enhancing the effective in multi-temperature applications. Enhancements through superior insulation, advanced controls, and auxiliary components like economizers minimize parasitic losses and optimize refrigerant flow. High-performance insulation materials and improved seals on pipes and components can reduce heat leakage by up to 10%, directly contributing to higher COP by preserving the temperature differentials essential for efficient cycling. Smart thermostats and control systems, leveraging sensors for real-time adjustment of setpoints and flow rates, further prevent overcooling or overheating, yielding COP improvements of 5-15% in variable-load environments. Economizers, such as those employing flash gas bypass, divert intermediate vapor to subcool the liquid refrigerant, enhancing evaporator performance and increasing COP by 4-14% in systems using microchannel evaporators or transcritical CO₂ cycles.

Advanced Metrics

Seasonal Coefficient of Performance

The Seasonal Coefficient of Performance () represents a time-averaged measure of for heating or cooling systems, such as heat pumps, over an entire season, incorporating variations in environmental conditions like outdoor . Unlike instantaneous values, accounts for the distribution of operating hours across different ranges, providing a more realistic assessment of annual by weighting the at each condition according to its occurrence. This metric is particularly relevant for systems exposed to fluctuating climates, where degrades at extreme . The calculation of SCOP follows standardized methodologies that divide the season into temperature "bins" based on historical climate data for specific regions. For each bin i, the COP (\text{COP}_i) is determined under part-load and full-load conditions, then multiplied by the number of hours (t_i) in that bin. The overall SCOP is the weighted average: \text{SCOP} = \frac{\sum (\text{COP}_i \times t_i)}{\sum t_i} This approach, detailed in the European standard EN 14825, ensures the metric reflects real-world usage patterns, including cycling losses and degradation at low temperatures, across average, warmer, or colder climate profiles. SCOP plays a critical role in regulatory frameworks, such as the European Union's energy labeling requirements for heat pumps, where it determines the energy efficiency class (from A+++ to G) under Regulation (EU) No 811/2013 and related ecodesign directives. By emphasizing seasonal performance over single-point tests, SCOP enables better consumer comparisons and supports policies aimed at reducing , as it captures the full impact of variable loads and ambient conditions on annual use. For example, a achieving a COP of 4 at standard conditions might yield an SCOP of 3.2 in a colder , where a greater proportion of operating hours occur at low temperatures, increasing auxiliary energy demands like defrosting.

Comparative Efficiency Measures

The coefficient of performance () serves as a fundamental, dimensionless metric for evaluating the efficiency of and systems, representing the of useful output to electrical or work input, typically expressed in SI units such as watts per watt (W/W). In contrast, the () measures cooling efficiency over a typical cooling season for air conditioners and , accounting for variations in outdoor temperature and part-load operation; it is expressed in British thermal units per watt-hour (BTU/Wh) and is mandated by U.S. Department of Energy () standards for equipment certification in . Since 2023, U.S. standards use updated testing procedures with SEER2, which is slightly more stringent than legacy ; values can be converted to an equivalent by dividing by approximately 3.412, reflecting the energy equivalence of 1 kWh to 3,412 BTU, though this conversion assumes steady-state conditions and does not fully capture seasonal dynamics. Similarly, the (HSPF) assesses heating for pumps across a heating season, defined as the total output in BTU divided by the total electrical input in watt-hours (BTU/Wh), paralleling SEER but for heating modes under U.S. regulations. HSPF can be approximated to a seasonal by multiplying by 0.293 (the inverse of 3.412), providing a comparable indicator, though HSPF emphasizes cumulative seasonal influenced by regional data. Since , HSPF2 is the current metric. This metric is particularly relevant for cold where pumps operate variably, unlike the point-specific measured at standard conditions like 47°F outdoor air. U.S. minimum standards, as of , require SEER2 ≥ 14.3 (equivalent to 15 SEER) and HSPF2 ≥ 7.5 (equivalent to 8.8 HSPF) for split systems. Beyond seasonal ratings, the Integrated Part Load Value (IPLV) evaluates efficiency for variable-capacity systems like chillers at partial loads, calculated as a weighted of COP or Energy Efficiency Ratio (EER) values at 100%, 75%, 50%, and 25% capacities, assuming typical operating hours distribution. IPLV is useful for applications with fluctuating demands, such as commercial buildings, where full-load COP may overestimate or underestimate real-world performance. The preference for COP in SI units globally stems from its unitless nature and alignment with the (SI), facilitating international standards and comparisons in design, as promoted by organizations like for consistent HVAC analysis worldwide. COP is ideally suited for fundamental thermodynamic analysis and system design due to its direct, condition-specific insight, while seasonal metrics like , HSPF, and IPLV are employed for consumer labeling, , and estimating annual energy costs in practical, variable environments. For instance, U.S. minimum standards require SEER2 ≥ 14.3 and HSPF2 ≥ 7.5 for split systems, emphasizing real-world applicability over idealized benchmarks. Seasonal , as a related over time, bridges these but remains distinct in its focus on continuous operation.

References

  1. [1]
    Refrigerators, air conditioners, and heat pumps
    For such a device we define the coefficient of performance COP as the ratio of the amount of heat removed at the lower temperature to the work put into the ...
  2. [2]
    3.4 Refrigerators and Heat Pumps - MIT
    A metric for devices of this type is the coefficient of performance, defined as. Figure 3.6: Operation of a Carnot refrigerator.
  3. [3]
    Heat Pump - HyperPhysics
    Heat Pumps are usually characterized by a coefficient of performance which is the number of units of energy delivered to the hot reservoir per unit work input.
  4. [4]
    Thermodynamics Glossary - Coefficient of Performance
    The pragmatic definition of the COP is: COP = (What you Get)/(What you Pay For). This measure of performance can have a value greater than unity, and it is ...
  5. [5]
    4.5 The Carnot Cycle – University Physics Volume 2
    Because the heat pump is assumed to be a Carnot pump, its performance coefficient is given by K P = Q h / W = T h / ( T h − T c ) . Thus, we can find the work W ...
  6. [6]
    [PDF] Lecture on Chapter 18: Heat Engines, Entropy, and the Second Law of
    The coefficient of performance for a refrigerator is the ratio of the heat ... COP(Carnot heat pump) =Thot. Thot - Tco¶d. (12). Example: If a refrigerator ...
  7. [7]
    No Title
    The thermal efficiency e of a heat engine ... Rather than efficiency, we talk about the coefficient of performance (COP) of refrigerators and heat pumps.<|control11|><|separator|>
  8. [8]
    [PDF] result desired achive input to Required result Desirded Measure e ...
    Since the refrigerator and heat pump cycles have different objectives, their performance measures, called coefficients of performance, are defined differently.
  9. [9]
    [PDF] Thermal efficiency - McGraw Commons
    Mar 27, 2013 · The reason for not using the term 'efficiency' is that the coefficient of performance can often be greater than 100%. Since these devices are ...
  10. [10]
    [PDF] Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics 3.4 ...
    ... define the coefficient of performance (COP) of the heat pump cycle, as the ratio of the amount heat added to the hot reservoir to the work done on the ...
  11. [11]
    15.5 Applications of Thermodynamics: Heat Pumps and Refrigerators
    What is considered the benefit in a heat pump is considered waste heat in a refrigerator. We thus define the coefficient of performance ( C O P ref ) of an ...<|control11|><|separator|>
  12. [12]
    Heat Transfer
    Thermodynamics is a branch of physics that deals with the energy and work of a system. Thermodynamics deals only with the large scale response of a system ...
  13. [13]
    [PDF] Notes on Thermodynamics, Fluid Mechanics, and Gas Dynamics
    May 15, 2024 · ... heat and work is that heat transfer occurs due to differences in temperature and work occurs through mechanical or electrical means. Heat ...
  14. [14]
    How heat pumps of the 1800s are becoming the technology of the ...
    Feb 15, 2023 · Heat pump efficiencies are generally measured in terms of their coefficient of performance, or COP. ... Lord Kelvin proposed using heat pump ...
  15. [15]
    Coefficient of performance: Meaning, Criticisms & Real-World Uses
    Oct 19, 2025 · The foundational principles underpinning the Coefficient of Performance can be traced back to the early 19th century with the work of French ...
  16. [16]
    [PDF] The Life and Legacy of William Rankine - Purdue e-Pubs
    The question of energy efficiency was uppermost in Rankine's mind as he developed his theories of prime movers for his text book in 1859. When the efficiency ...
  17. [17]
    Air Conditioning and Refrigeration Timeline | ashrae.org
    Thomas Moore of Maryland received US patent for refrigerator. First patent issued in US on refrigeration. 1805. Oliver Evans proposed a closed cycle vapor ...
  18. [18]
    What is ASHRAE Standard 90.1? - Van Meter Inc.
    Apr 6, 2021 · In 1975, ASHRAE 90-75: Energy Conservation in New Building Design was published as the first national energy code. Later, as part of the 1989 ...
  19. [19]
    [PDF] Thermodynamics equation
    Coefficient of Performance for HP, COPHP. COPHP = Desired output. Required input. = QH. Wnet,in. COPHP = QH. QH ...
  20. [20]
    [PDF] Intro to thermodynamics Name: A power cycle produces 2.4 × 108 ...
    η = 25.26%. Thermal efficiency vs. Coefficient of Performance page 1 of 3 prepared by Dr. Narendranath. Page 2. MEEM2201: Intro to thermodynamics. Name: An ...
  21. [21]
    Coefficients of Performance - AQA A Level Physics Revision Notes
    Apr 8, 2025 · Step 1: State the First Law of Thermodynamics (for reversed heat engine) · Step 2: Determine · Step 3: Substitute into the First Law to determine ...
  22. [22]
    Energy, Enthalpy, and the First Law of Thermodynamics
    E is negative when the system does work on its surroundings. The sign conventions for heat, work, and internal energy are summarized in the figure below.
  23. [23]
    Introduction to the First Law - Chemistry 301
    The negative sign is to keep our sign convention for energy going into or out of the system. Expansion will lower the energy of the system (energy out). Since ...
  24. [24]
    [PDF] 4.2 Refrigerators - Physics
    To avoid confusion with equation 4.1, this ratio is called the coefficient of performance: COP = benefit cost. = Qc. W . (4.6). Just as for a heat engine, we ...
  25. [25]
    Heat Pumps and Refrigerators – College Physics chapters 1-17
    To calculate the heat pump's coefficient of performance, use the equation C O P hp = Q h W . A refrigerator is a heat pump; it takes warm ambient air and ...
  26. [26]
    [PDF] HEAT ENGINES
    COP x x x x. NOTE THAT: Coefficient of Performance values are generally > 1. Also, it can be shown that: COPHP = COPR + 1. Since. HP. L. H. H. L. H. L. R. COP.
  27. [27]
  28. [28]
    [PDF] Unit 7 – Second Law Introduction October 19, 2010 ME 370 ... - CSUN
    law, results for Carnot cycles are used to derive entropy. • Here we will show that Carnot cycle results can be obtained from principle that dSisolated ...
  29. [29]
    4.5 The Carnot Cycle – General Physics Using Calculus I
    during this isothermal expansion. With the first law of thermodynamics, Δ E ... for the coefficient of performance of the ideal-gas Carnot refrigerator.
  30. [30]
    Reversible and irreversible heat engine and refrigerator cycles
    May 1, 2018 · Actual heat engines and refrigerators have unavoidable sources of irreversibility like friction and heat leaks. They typically operate so fast ...Missing: below | Show results with:below
  31. [31]
    Optimization Modeling of Irreversible Carnot Engine from the ...
    External irreversibilities are due to heat transfer at temperature gradient between the cycle and heat reservoirs, while internal ones are represented by ...
  32. [32]
    [PDF] Energy, exergy, and Second Law performance criteria
    and then the Second Law efficiency of the system is. ηII ¼ ηI=ηI;rev ¼ 60:3%; 2:7% higher than the exergy efficiency despite the smallness of the difference ...
  33. [33]
    Energy and Exergy Analysis of Refrigeration Systems - IntechOpen
    Since T0=TH for a refrigeration cycle, thus, the second-law efficiency is also equal to the ratio of actual and maximum COPs for the cycles, which accounts for ...Missing: typical commercial
  34. [34]
    [PDF] Second-Law Analysis to Improve the Energy Efficiency of Screw ...
    second-law efficiency and the coefficient of ... 30%. 40%. 50%. 60%. 70%. 80%. 90%. 100%. Unit A. Unit B ... heat pump greenhouse heating system. Energ. Bldg ...<|control11|><|separator|>
  35. [35]
  36. [36]
    Indirect Electrochemical Cooling: Model-Based Performance ... - NIH
    Jan 2, 2024 · Temperature of the heat sink Tsink = 35 °C. Minimum approach temperature for the electrochemical cell and evaporator ΔTapproach = 5 K.
  37. [37]
    Evaluation of pressure drop effect on COP of single-stage vapor ...
    Feb 1, 2022 · This paper addresses a theoretical investigation about the effect of pressure drop along the heat exchangers on the coefficient of performance, heat transfer ...
  38. [38]
    Vapor Compression Cycle: A State-of-the-Art Review on ... - MDPI
    This study presents the latest developments in the vapor compression cycle and natural refrigerants, focusing on water as a refrigerant.<|control11|><|separator|>
  39. [39]
    Performance evaluation of air-source heat pump based on a ... - NIH
    Feb 9, 2024 · The coefficient of performance (COP) of a an air-source heat pump is influenced by ambient temperature, to a lesser degree by relative humidity ...
  40. [40]
    [PDF] Empirical Study of the Effect of Thermal Loading on the Heating ...
    Jan 18, 2023 · It should be noted that there are other factors that affect heat pump efficiency besides the outdoor temperature and level of thermal loading. ...
  41. [41]
    [PDF] Properties of Refrigerant Affect Compressor Design - Purdue e-Pubs
    Jul 19, 2012 · Refrigerant properties like volumetric capacity, pressure difference, and isentropic coefficient of performance affect compressor design. Lower ...
  42. [42]
    Refrigerant Performance Evaluation Including Effects of Transport ...
    May 19, 2017 · The dominant property affecting pressure drop is the vapor density, where a high value results in low pressure drop, Δp, and low saturation ...
  43. [43]
    [PDF] performance limits of the vapor compression cycle
    The level of COP improvement depends on a refrigerant's thermodynamic properties and varies from cycle to cycle. (Domanski, 1995). In this study we explore the ...
  44. [44]
    [PDF] Thermodynamic Assessment of High-Temperature Heat Pumps for ...
    Jul 17, 2014 · Table 4 shows the effect of the compressor efficiency and the heat exchanger size on the overall COP to set the lowest limit of development ...Missing: impact | Show results with:impact
  45. [45]
    [PDF] Proceedings of the DOE Heat Pump Contractors' Program ...
    Doubling the total heat exchanger area yields an increase of 15% in predicted COP over the optimum configurations with smaller condensers and evaporators for ...Missing: impact | Show results with:impact
  46. [46]
    (PDF) The impact of the work under partial load on the energy ...
    The reason of this is the operation of the device under partial load. Although the values of COP were very high in short periods of operation, frequent ...Missing: non- | Show results with:non-
  47. [47]
    [PDF] Experimental Study of Compressor Modulation Method Effects on ...
    The study evaluates single speed, variable speed, and uneven tandem compressor arrangements to test their effects on heat pump performance.Missing: non- | Show results with:non-
  48. [48]
    [PDF] Part-Load Performance Characterization and Energy Savings ...
    This report documents the development of part- load performance curves and there use with the EnergyPlus simulation tool to estimate the potential savings from ...Missing: non- | Show results with:non-
  49. [49]
    [PDF] Thermodynamic Cycle Analysis and Experimental Investigate on a ...
    Jul 14, 2016 · Heating capacity and COP of the two-stage vapor injection ASHP were improved up to 30%~40% and 20% (Wang, 2009 & Shen, 2015), respectively, as ...
  50. [50]
    Pros in the use of the natural refrigerant CO2 in refrigeration | CAREL
    CO2 is cheap, green, has a low critical temperature, and is better in subcritical conditions with high density and thermal conductivity.
  51. [51]
    [PDF] Benefits and Challenges in Using Low GWP A3 Refrigerants in ...
    An estimated savings of $44.50 per ton of carbon dioxide equivalent is possible due to lower operating costs of R-290 due to higher energy efficiency than ...
  52. [52]
    Performance Enhancement Analysis of Environmentally Friendly ...
    Apr 29, 2024 · This study examines the coefficients of performance of 21 currently available refrigerants with very low global-warming potential and zero ozone-depleting ...
  53. [53]
    Theoretical study of an auto-cascade high-temperature heat pump ...
    The improved auto-cascade cycle exhibited a COP increase of 18.17%-37.4% compared to the basic cycle and 6.3%-21.2% compared to the basic auto-cascade cycle. ...
  54. [54]
    [PDF] Multi-Temperature Heat Pumps - A Literature Review - Purdue e-Pubs
    The performance of the cycles is compared in terms of First Law efficiency (COP) and Second Law efficiency (exergy) using simplified thermodynamic simulations.
  55. [55]
    When and how to use cascade high temperature heat pump—Its ...
    Jun 1, 2024 · Cascade configuration is commonly considered suitable for high temperature heat pump when there is significant temperature difference between heat source and ...<|separator|>
  56. [56]
    Simultaneous use of air-side and water-side economizers with the ...
    Specifically, by optimizing free cooling operation and thermal insulation the cooling energy consumption can be decreased up to 80% and 10%, respectively ...
  57. [57]
    [PDF] HVAC Technology Guide - Bonneville Power Administration
    Jan 1, 2018 · An inverter driven compressor can modulate capacity to match the heating load. Beginning in 2006, a number of Asian manufacturers introduced ...
  58. [58]
    "Flash Gas Bypass Method for Improving Performance of an A/C ...
    This paper demonstrates that Flash Gas Bypass (FGB) method significantly improved the performances of the microchannel evaporator and the system, ...Missing: insulation smart controls economizers
  59. [59]
    Advancements in vapor compression air conditioning systems for ...
    Oct 20, 2025 · [235] reported that using a flash tank economizer improved cooling capacity and COP by 14% and 4%, respectively. However, IHXs provided ...
  60. [60]
    Seasonal Performance Factor - an overview | ScienceDirect Topics
    The SCOP is a weighted average of COPs over a range of outside air conditions following a specific test method, according to European Standard EN 14825. The ...
  61. [61]
    [PDF] Labelling and certification of HVAC products - rehva
    For heat-pumps the energy class is based on the SCOP. EU energy labels in preparation. Other HVAC products are likely to be covered by an EU en- ergy label ...<|control11|><|separator|>
  62. [62]
    Understanding SCOP vs COP in Heat Pumps - GOODHEAT
    Jul 5, 2025 · For example, a unit with a COP of 4 may only deliver a SCOP of 3 in colder climates due to frequent defrosting or longer compressor runtimes.
  63. [63]
    Key Performance Metrics for Heating and Cooling Equipment
    The Seasonal Energy Efficiency Ratio (SEER) provides a better estimate of actual performance, accounting for outdoor temperature variation. Seasonal Energy ...Energy Efficiency Ratio... · Integrated Energy Efficiency... · Energy Factor (ef)<|separator|>
  64. [64]
    Heat Pumps - Performance and Efficiency Ratings
    HSPF of 6.8 can be compared with an average COP of 2. A HSPF in the range of 5-7 is acceptable. Example - Heat Pump Heating Season Performance Factor. For a ...<|separator|>
  65. [65]
    SEER vs HSPF vs (S) COP Heat Pump Ratings - How to Compare
    Apr 9, 2023 · HSPF stands for Heating Seasonal Performance Factor, which is a measure of the efficiency of a heat pump's heating mode during the heating ...
  66. [66]
    How to Calculate Chiller IPLV - MEP Academy
    It is based on part load chiller efficiency values. The IPLV is calculated on the weighted percentage of assumed operational hours at each operating condition.
  67. [67]
    Heat Pump Equipment and Central ACs Key Product Criteria
    SEER2 is the total heat removed from the conditioned space during the annual cooling season, expressed in Btu, divided by the total electrical energy consumed ...
  68. [68]
    [DOC] heating efficiency
    c Heating Seasonal Performance Factor (HSPF) is the total space heating required in U.S. climate region IV (mixed dry climate) during the space heating season, ...